Fractal dimension and lacunarity of tractography images of the human brain

Fractals

Volumn 17, Issue 2, 2009, Pages 181-189

  Katsaloulis, P ^a   Verganelakis, D A ^b   Provata, A ^a  

^a Institute of Physical Chemistry Demokritos National Centre for Scientific Research   (Greece)

^b Institute EUROMEDICA ENCEPHALOS   (Greece)

Author keywords

Diffusion; Fractal dimension; Lacunarity; MRI; Neuron tracts; Tensor imaging; Tractography

Indexed keywords

BRAIN; DIFFUSION TENSOR IMAGING; FRACTAL DIMENSION; NEURONS; TENSORS;

BOX-COUNTING; HUMAN BRAIN; LACUNARITY; NEURON AXON; NEURON TRACT; PROPERTY; SELF-SIMILAR; SYSTEM RESOLUTION; TENSOR IMAGING; TRACTOGRAPHY;

MAGNETIC RESONANCE IMAGING;

EID: 68249090373     PISSN: 0218348X     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218348X09004284     Document Type: Article

References (29)

1. S. Ogawa, T. M. Lee, A. R. Kay and D. W. Tank, Brain magnetic resonance imaging with contrast dependent on blood oxygenation, Proc. Natl. Acad. Sci. USA 87 (1990) 9868-9872.
2. K. K. Kwong, J. W. Belliveau, D. A. Chesler, I. E. Goldberg, R. M. Weisskoff, B. P. Poncelet, D. N. Kennedy, B. E. Hoppel, M. S. Cohen and R. Turner, Dynamic magnetic resonance imaging of human brain activity during primary sensory stimulation, Proc. Natl. Acad. Sci. USA 89 (1992) 5675-5679.
3. R. J. Scheck, E. M. Coppenrath, M. W. Kellner, K. J. Lehmann, C. Rock, J. Rieger, L. Rothmeier, F. Schweden, A. A. Bauml and K. Hahn, Radiation dose and image quality in spiral computed tomography: Multicentre evaluation at six institutions, Brit. J. Radiol. 71 (1998) 734-744.
4. D. A. Sipkins, D. A. Cheresh, M. R. Kazemi1, L. M. Nevin, M. D. Bednarski1 and K. C. P. Li, Detection of tumor angiogenesis in vivo by avb 3-targeted magnetic resonance imaging, Nat. Med. 4 (1998) 623-626.
5. T. Sugahara, Y. Korogi, M. Kochi, I. Ikushima, Y. Shigematu, T. Hirai, T. Okuda, L. Liang, Y. Ge, Y. Komohara, Y. Ushio and M. Takahashi, Usefulness of diffusion-weighted MRI with echo-planar technique in the evaluation of cellularity in gliomas, J. Mag. Res. Imag. 9 (1999) 53-69.
6. A. E. Wefera, H. Hricaka, D. B. Vigneron, F. V. Coakleya, Y. Lua, J. Wefera, U. Mueller-Lissea, P. R. Carrolla and J. Kurhanewicz, Sextant localization of prostate cancer: Comparison of sextant biopsy, magnetic resonance imaging and magnetic resonance spectroscopic imaging with step section histology, Clin. Urol. 164 (2000) 400-4004.
7. P. J. Basser, J. Mattiello and D. LeBihan, MR diffusion tensor spectroscopy and imaging, Biophy. J. 66 (1994) 259-267.
8. P. J. Basser, S. Pajevic, C. Pierpaoli, J. Duda and A. Aldroubi, In vivo fiber tractography using DT-MRI data, Mag. Res. Med. 44 (2000) 625-632.
9. M. Jackowskia, C. Y. Kaod, M. Qiua, R. T. Consta-blea and L. H. Staib, White matter tractography by anisotropic wavefront evolution and diffusion tensor imaging, Med. Image Anal. 9 (2005) 427-440.
10. M. D. Denis Le Bihan, J. F. Mangin, C. Poupon, C. A. Clark, S. Pappata, N. Molko and H. Chabriat, Diffusion tensor imaging: Concepts and applications, J. Mag. Res. Imag. 13 (2001) 534-546.
11. E. R. Melhem, S. Mori, G. Mukundan, M. A. Kraut, M. G. Pomper and P. C. M. van Zijl, Diffusion tensor MR imaging of the brain and white matter tractog-raphy, Am. J. Roentgenol. 178 (2002) 3-16.
12. A. Eshel, On the fractal dimensions of a root system, Plant Cell Environ. 21 (1998) 247-251.
13. E. Guyon and H. E. Stanley, Fractal Forms (Elsevier; North Holland, 1991).
14. H. F. Jelinek and E. Fernandez, Neurons and fractals: How reliable and useful are calculations of fractal dimensions? J. Neurosci. Method. 81 (1998) 9-18.
15. F. Family, B. R. Masters and D. E. Platt, Fractal pattern formation in human retinal vessels, Physica D 38 (1989) 98-103.
16. D. A. Cameron, H. Vafai and J. A. White, Analysis of dendritic arbors of native and regenarated ganglion cells in the goldfish retina, Visual Neurosci. 16 (1999) 253-261.
17. R. J. T. Wingate, T. Fitzgibbon and I. D. Thompson, Lucifer yellow, retrograde tracers and fractal analysis characterise adult ferret retinal ganglion cells, J. Comp. Neurol. 323 (1992) 449-474.
18. R. J. T. Wingate and I. D. Thompson, Axonal target choice and dendritic development of ferret beta retinal ganglion cells, Eur. J. Neurosci. 7 (1995) 723-731.
19. L. A. Coleman and M. J. Friedlander, Postnatal dendritic development of y-like geniculocortical relay neurons, Int. J. Dev. Neurosci. 20 (2002) 137-159.
20. M. F. Shlesinger and B. J. West, Complex fractal dimension of the bronchial tree, Phys. Rev. Lett. 67 (1991) 2106-2108.
21. F. Caserta amd W. D. Eldred, E. Fernandez, R. E. Hausman, L. R. Stanford, S. V. Bulderev, S. Schwarzer and H. E. Stanley, Determination of fractal dimension of physiologically characterized neurons in two and three dimensions, J. Neurosci. Method. 56 (1995) 133-144.
22. G. B. West, J. H. Brown and B. J. Enquist, A general model for the origin of allometric scaling laws in biology, Science 276 (1997) 122-126.
23. M. Zamir, Fractal dimensions and multifractility in vascular branching, J. Theor. Biol. 212 (2001) 183-190.
24. B. J. West, Fractal Physiology and Chaos in Medicine (World Scientific, Singapore, 1990).
25. R. E. Plotnick, R. H. Gardner, W. W. Hargrove, K. Prestegaard and M. Perlmutter, Lacunarity analysis: A general technique for the analysis of spatial patterns, Phys. Rev. E 53 (1996) 5461-5468.
26. G. Landini, P. I. Murray and G. P. Misson, Local connected fractal dimensions and lacunarity analyses of 60? fluorescein angiograms, Invest. Ophthalmol. Vis. Sci. 36 (1995) 2749-2755.
27. G. A. Tsekouras and A. Provata, Nonextensivity of the cyclic lattice lotka-volterra model, Phys. Rev. E 65 (2002) 016-204.
28. J. Feder, Fractals (Plenum Press, 1989).
29. H. Takayasu, Fractals in Physical Science (Manchester University Press, 1991).